Question

find two numbers whose sum is 27 and product is 182​

Answer 1

Answer:

$x = 13 \: and \: 14\\y=13 and 14$✔✔

Step-by-step explanation:

SOLUTION-

$let \: the \: two \: number \: be \:x \: and \: y \\ x + y = 27 - - - - - (2) \\ x \times y = 182 \\ y = \frac{182}{x} - - - - - (1) \\ putting \: value \: of \: x \: in \: (1) \\ x + \frac{182}{x} = 27 \\ \frac{ {x}^{2} + 182}{x} = 27 \\ {x}^{2} + 182 = 27x \\ {x}^{2} - 27x + 182 = 0 \\ {x}^{2} - 14x - 13x + 182 = 0 \\ x(x - 14) - 13(x - 14) = 0 \\ (x - 13)(x - 14) = 0 \\ (x - 13) = 0 \\ x = 13 \\ x - 14 = 0 \\ x = 14\\putting value of x in (1)\\14+y=27\\y=13\\13+y=27\\y=14$

Answer 2

SOLUTION :

Let the numbers be x and y

Sum of two numbers = 27

x + y = 27

x = 27 - y ------(1)

Product of those numbers = 182

xy = 182 --------(2)

Substitute eq - (1) in eq - (2)

(27 - y)y = 182

27 y - y² = 182

y² - 27y = 182

y² - 27y - 182 = 0

Split the middle terms.

y² - 14y - 13y - 182 = 0

y(y - 14) - 13(y - 14) = 0

y - 14 = 0 ; y - 13 = 0

y = 14 ; y = 13

Take any number

y = 14

Substitute y in eq - (2)

xy = 182

(14)x = 182

x = 182/14

x = 13

Therefore, the two numbers are 13 and 14.